Final Answer:
(a) The tension in cable AC is TAC = W / (2 * cos(α)), where W is the weight applied.
(b) The tension in cable BC is TBC = W / (2 * sin(α)).
Step-by-step explanation:
(a) To find the tension in cable AC, we consider the vertical equilibrium of the system. The weight W is distributed equally between cables AC and BC. Applying the cosine component of the weight along cable AC, we use the equation TAC * cos(α) = W / 2. Solving for TAC, we get TAC = W / (2 * cos(α)).
(b) For the tension in cable BC, we use the sine component of the weight along cable BC. The equation TBC * sin(α) = W / 2 represents the vertical equilibrium. Solving for TBC, we obtain TBC = W / (2 * sin(α)).
In both cases, the trigonometric functions account for the component of the weight acting along each cable. These equations provide the tensions in cables AC and BC based on the given angle α. The approach ensures accurate determination of the tensions, taking into account the forces involved in the loaded system.
In conclusion, the tensions in cables AC and BC are determined by analyzing the vertical equilibrium and applying trigonometric principles. The resulting equations express the tensions in terms of the weight and the angle α, providing a comprehensive solution to the problem.